Dr. Tarakanta Nayak

Associate Professor

School of Basic Sciences

Office : 329, SBS Building

Phone : 674-713-5166

Email : tnayakATiitbbsDOTacDOTin

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Education

Degree	Discipline	Year	School
Ph.D.	Mathematics	2001-2006	Indian Institute of Technology Guwahati
Post doc	Mathematics	2008-2009	School of Mathematical Sciences, Tsinghua University, Beijing

Research Interests

Complex Dynamics; Fractals; Independence polynomials and Independent fractals of graphs

Teaching

Math-I, Math-II, Transform Calculus, Probability, Statistics & Stochastic Processes, Complex Analysis, Fractals, Advanced Complex Analysis, Complex Dynamics, Linear Algebra, Discrete Mathematics

Publications

Journals

1Subhasis Ghora and Tarakanta Nayak, On Fatou sets containing Baker omitted value, Accepted, Journal of Dynamics and Differential Equations(2021)

2Tarakanta Nayak, Polynomials through pictures, Resonance (September 2021)

3Subhasis Ghora and Tarakanta Nayak, On periods of Herman rings and relevant poles, Indian J Pure Appl Math (2021). https://doi.org/10.1007/s13226-021-00112-w.

4Rajen Kumar and Tarakanta Nayak, The Real Non-attractive Fixed Point Conjecture and Beyond, Mathematics Newsletter, 31 (Sept 2020), no. 2, 64-71.

5Sasmita Barik, Tarakanta Nayak and Ankit Pradhan, Graphs whose independent fractals are line segments, Bulletin of the Malaysian Mathematical Sciences Society, 44(1), 55-78 (2020) https://doi.org/10.1007/s40840-020-00936-5

6Tarun Kumar Chakra and Tarakanta Nayak, Iteration of the translated tangent, Bulletin of the Malaysian Mathematical Sciences Society, 42 (2019), no. 5, 1993-2008.

7Tarun Kumar Chakra, Gorachand Chakraborty and Tarakanta Nayak, Herman rings with small periods and omitted values, Acta Mathematica Scientia, Series B, 38 (2018), no. 6, 1951-1965

8Tarun Kumar Chakra, Tarakanta Nayak and Kedarnath Senapati, Iteration of certain exponential-like meromorphic functions, Proceedings of Indian Academy of Sciences (Mathematical Sciences), 128 (2018), no. 5, Art. 64, 18 pp.

9Tarun Kumar Chakra, Gorachand Chakraborty and Tarakanta Nayak, Baker omitted value, Complex Variables and Elliptic Functions, 61 (2016), no. 10, 1353 - 1361.

10Tarakanta Nayak, Herman rings of meromorphic maps with an omitted value, Proceedings of the American Mathematical Society, 144 (2016), no. 2, 587 - 597.

11Tarakanta Nayak, On Fatou components and omitted values, Geometry, groups and dynamics, 349 - 358, Contemporary Mathematics, 639, American Mathematical Society, Providence, RI, 2015.

12Tarakanta Nayak and M. Guru Prem Prasad, Julia sets of Joukowski-exponential maps, {\it Complex Analysis and Operator Theory}, 8 (2014), no.5, 1061--1076.

13Tarakanta Nayak and Jian-Hua Zheng, Omitted values and dynamics of meromorphic functions, Journal of London Mathematical Society, (2) 83 (2011), no.1, 121--136.

14Tarakanta Nayak and M. Guru Prem Prasad, Iteration of certain meromorphic functions with unbounded singular values, Ergodic Theory and Dynamical Systems, 30 (2010), no.3, 877--891.

15Tarakanta Nayak and Zheng Jian Hua, Omitted values and dynamics of meromorphic functions, Abstracts, International Congress of Mathematicians, 19–27 August, 2010, 313

16 M. Guru Prem Prasad and Tarakanta Nayak, Dynamics of $\lambda \tanh (e^z)$, Discrete and Continuous Dynamical Systems Series A, 19 (2007), no.1, 121--138.

17 M. Guru Prem Prasad and Tarakanta Nayak, Dynamics of certain class of critically bounded entire transcendental functions, Journal of Mathematical Analysis and Applications, 329 (2007), no.2, 1446--1459.

18Tarakanta Nayak and M. Guru Prem Prasad, Bifurcation and chaotic burst in the dynamics of $\lambda e^{b z + c e^z}$, Journal of Combinatorics, Information and System Sciences, 28/29 (2003/2004), 211--226.

19Exploding Julia sets in the dynamics of f ?(z) = ?J1(iz)/iz, Proceedings of The Third National Conference on Non-linear Systems and Dynamics, (NCNSD-2006), 171-174, Allied Publishers Pvt. Ltd.

Conferences

1 Baker omitted value, Invited talk in 34 th Annual Conference of the Ramanujan Mathematical Society, 1-3 August 2019, Pondicherry University, Punducherry, India

2Independence fractal of a graph, Invited talk in 83rd Annual Conference of Indian Mathematical Society, 12-15 Dec 2017, Sri Venkateswar University, Tirupati, Andhra Pradesh, India

3Completely invariant domains, Complex Analysis: Geometric and Dynamical Aspects, Non 14-19, 2016, Centre of Excellence in Mathematical Sciences, Almora, India

4Complex Dynamics of some simple maps, National Workshop on Topological Dynamics Dec 10 -- 12, 2015, National Institute of Technology, Karnataka, Surathkal, India

5Herman rings, Frontiers in Complex Dynamics, Dec 19 -- 20, 2012, University of Barcelona, Spain

Academic Honors & Awards

Ramanujan Prize for 2018 given by Ramanujan Institute for Advanced Study in Mathematics, University of Chennai
Member of INYAS (Indian National Young Academy of Science), 2018-2022
Junior Associate of International Centre for Theoretical Physics, Italy for the period 2012-2017

PhD

Completed: 1 (Tarun Kumar Chakra)

Continuing: 2 (Subhasis Ghora and Soumen Pal)

MSc projects for students of IIT Bhubaneswar

Completed: 12

Continuing: 2

MSc and BTech projects for other students

Completed: 4

Professional Activities

Reviewer, Mathematical Reviews (Published by American Mathematical Society)
Regional Coordinator (Odisha), Madhava Mathematics Competition (since 2015)
Acted as supervisor for Joint Science Academies' Summer Research Fellowship Programme
Member, Board of studies, Salipur Autonomous College, Salipur (2014-2016)
Zonal coordinator, Indian National Mathematical Olympiad for Utkal University zone
Member in the interview board for selection of Trained Graduate Teachers in Kendriya Vidyalaya Sangathan on 30 April, 2011

Student Supervision

PhD: Soumen Pal and Sukanta Das (continuing)

Subhasis Ghora (Thesis submitted in 2022)

Tarun Kumar Chakra, 2018 (Thesis: Iteration of meromorphic functions with an omitted value)

Post Doc: Dr Kedarnath Senapati , 2014-2016

MSc:

14. Dynamics of Reduced Independence polynomials, 2021-22

13. Line segments as independence fractals, Saikat Giri, 2019-20

12. Fixed points and their multipliers for a polynomial, Rajen Kumar, 2018-19.

11. Graphs whose independence fractals are line segments, Sanjoy Mondal, 2018-19

10. Quasiconformal mapping and No wandering theorem, Abhisek Pandey, 2018-19

9. Fractal Transformation using Iterated Function System, Chavan Ratan, 2017-18

8. Quasiconformal mappings, Garima Gupta, 2016-17

7. A study of roots of Independence polynomials, Vijay Kumar Meena, 2016-17

6. The Independence fractal of a graph, Kartik Pandey, 2016-17

5. Finding all roots of a polynomial by Newton's Method, Soumen Pal, 2015-16

4. A study on palindromic polynomials, Priti Prasanna Mondal, 2015-16

3. Polynomial root finding, Anudeep Nain, 2014-15

2. The Julia sets of relaxed Newton method for polynomials with two roots, Satyabrata Jana, 2014-15

1. Dynamical behaviour of multiply connected Fatou components of transcendental entire functions, Jogender Singh, 2014-15.

Summer and Winter projects:

4. Roots of Chromatic Polynomials, winter project by Labhansh Gemini, NIT Hamirpur, 11-31 Dec 2018

3. The independence polynomial of a graph, summer project by Satyabrat Rath, NIT Rourkela, 2018

2. On Herman rings of transcendental meromorphic functions, summer project by Pranav Kumar Upadrasta, IIT Kharagpur (under SRF Programme - 2014, jointly sponsored by IASc-Bangalore, INSA-New Delhi and NSAI-Allahabad).

1. When two fractals are the same, summer project by Prashant Kumar Ojha, NIT Rourkela during May 15 -- July 15, 2011.